How To Measure Velocity and Thrust
In order to fully grasp the concepts behind the mechanics of a water-air propelled bottle rocket, theoretical and experimental aspects must be considered. The equations for velocity and thrust at takeoff are known but seeing a rocket take off and being able to back up your theoretical findings with experimental data is important. Without the help of expensive, high-tech measurement devices, data can still be captured.
In order to measure the velocity at take off, a few things are needed. The first is a meter stick or yardstick and the second is any smartphone with slow motion capture capabilities. Position the rocket next to a vertically standing meter stick or yardstick. Commence with usual liftoff procedures. Set smartphone to slow motion capture mode and face it towards the rocket with the meter stick or yardstick in view. After the rocket has taken off and safely landed, look at the slow motion footage and make some calculations. As the rocket propels itself up, it displaces in the y - direction. As this displacement occurs, time elapses.
Though, in theory this equates to average velocity since no derivative was taken, but since the change in time Δt, is so small, the result is still accurate.
When shifting focus to the measurement of thrust, the calculation is not as simple. Since thrust is the measurement of the expulsion of mass but is measured in weight, an experiment can be set up to measure thrust. Use a meter stick or a yardstick, a smartphone with slow motion capabilities, and three identical springs with known spring constants and known equilibrium lengths. Attach the spring to the bottom of each fin, assuming there are three fins. Commence with usual liftoff procedures. Set smartphone to slow motion capture mode and face it towards the rocket with the estimated approximate height on the measuring stick in view. Let the rocket run its course and take a look at the footage. The springs should allow the rocket to reach a certain height and then the rocket returns to the ground. This height should be able to be seen in the slow motion footage. Take that value as the maximum elongation of the spring and set up a sum of the forces equation using Newton’s Second Law.